CIF: Small: Collaborative Research: Between Shannon and Hamming

在过去的70年里，信息理论和编码使通信技术对日常生活产生了惊人的影响。由于编码/解码策略与通信信道的相应模型之间的匹配，这是可能的。传统的模型处于两个极端。假设信道是随机的模型，例如那些涉及由无记忆随机过程控制的信道噪声的模型，采用信道的平均情况视图：这种模型是香农理论的基础。在另一个极端，类似“汉明”的模型采用通道的最坏情况视图：噪声可以相对于通信方案进行逆向选择。然而，对于一些现有的和新兴的通信系统，香农/平均情况的观点可能过于乐观，而汉明/最坏情况的观点可能过于悲观。这个项目承担了研究位于香农和汉明极端之间的模型的挑战。这项研究的结果将为许多实际设置的代码设计提供信息，这些设置中的平均情况干扰模型可能过于乐观，而最坏情况模型可能过于悲观，例如车载网络（VANETS）或物联网（IoT）中的无线多帧通信系统。看待平均情况和最坏情况分析之间区别的常见方法是操作性的：它是误差标准的不同。这个项目采取了不同的观点：不同之处在于干扰如何依赖于传输的码字。这是通过假设干扰由干扰机控制来建模的。一个依赖干扰机对应于汉明模型，而一个独立干扰机对应于香农模型。限制干扰机的干扰如何依赖于传输的码字，产生了介于香农和汉明之间的模型。该项目为研究干扰机在不同程度不确定性下的通信模型奠定了理论基础，并确定了新的信道模型、代码设计和容量概念。该项目将对Shannon和Hamming模型之间的信道模型进行统一处理，并能够(a)设计利用干扰器限制的最佳速率编码方案；(b)设计安全的通信方案，利用干扰器的限制来改善传统的容量和安全性之间的权衡；(c)为未来实用规范的设计提供参考。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Over the last 70 years, information theory and coding have enabled communication technologies that have had an astounding impact on everyday lives. This is possible due to the match between encoding/decoding strategies and corresponding models of the communication channel. Traditional models fall at two ends of a spectrum. Models which assume that the channel is random, such as those involving channel noise governed by a memoryless stochastic process, take an average-case view of the channel: such models are the basis of Shannon theory. At the other extreme, "Hamming"-like models take a worst-case view of the channel: the noise can be chosen adversarially with respect to the communication scheme. However, for several existing and emerging communication systems, the Shannon/average-case view may be too optimistic, whereas the Hamming/worst-case view may be too pessimistic. This project takes up the challenge of studying models that lie between the Shannon and Hamming extremes. The outcomes of this research will inform the design of codes for a multitude of practical settings where average-case interference models may be too optimistic and worst-case models may be too pessimistic, such as wireless multiple-frame communication systems in vehicular networks (VANETS) or the Internet of Things (IoT).The common way to view the distinction between average-case and worst-case analysis is operational: it is a difference in error criterion. This project takes a different perspective: the difference is in how the interference can depend on the transmitted codeword. This is modeled by assuming the interference is controlled by a jammer. A dependent jammer corresponds to the Hamming model while an independent one corresponds to that of Shannon. Restricting how jammer interference can depend on the codeword transmitted gives rise to models that lie between those of Shannon and Hamming. The project develops theoretical foundations for the study of communication models in which the jammer acts under varying degrees of uncertainty, and identifies new channel models, code designs, and capacity concepts. The project will develop a unified treatment of channel models that lie between the Shannon and Hamming model and abilities to (a) design optimal rate coding schemes that utilize the limitations posed on the jammer; (b) design secure communication schemes that leverage the jammer's constraints to improve traditional tradeoffs between capacity and security; and (c) inform the design of future practical codes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.